Global value numbering using random interpretation

We present a polynomial time randomized algorithm for global value numbering. Our algorithm is complete when conditionals are treated as non-deterministic and all operators are treated as uninterpreted functions. We are not aware of any complete polynomialtime deterministic algorithm for the same problem. The algorithm does not require symbolic manipulations and hence is simpler to implement than the deterministic symbolic algorithms. The price for these benefits is that there is a probability that the algorithm can report a false equality. We prove that this probability can be made arbitrarily small by controlling various parameters of the algorithm. Our algorithm is based on the idea of random interpretation, which relies on executing a program on a number of random inputs and discovering relationships from the computed values. The computations are done by giving random linear interpretations to the operators in the program. Both branches of a conditional are executed. At join point...

• Type: Conference
• Year: 2004
• Where: POPL
• Authors: Sumit Gulwani, George C. Necula
• Keywords: Analysis This Research, Global Value Numbering, National Science Foundation, POPL 2004, Programming Languages